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A003295
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McKay-Thompson series of class 11A for the Monster group with a(0) = -5.
(Formerly M3872)
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5
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1, -5, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666
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OFFSET
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-1,2
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COMMENTS
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Coefficients of a modular function denoted by B(tau) in Atkin (1967).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Expansion of -11 + (1 + 3*F)^2 * (1/F + 1 + 3*F) where F = eta(q^3) * eta(q^33) / (eta(q) * eta(q^11)) (= g.f. of A128663) in powers of q.
G.f. is Fourier series of a level 11 modular function. f(-1 / (11 t)) = f(t) where q = exp(2 Pi i t).
A000521(n) = a(n) + 11 * a(11*n) unless n=0. [Atkin (1967) p. 22]
a(n) ~ exp(4*Pi*sqrt(n/11)) / (sqrt(2)*11^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
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EXAMPLE
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G.f. = 1/q - 5 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...
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MATHEMATICA
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QP = QPochhammer; F = q*QP[q^3]*(QP[q^33]/(QP[q]*QP[q^11])); s = q*(-11 + (1 + 3*F)^2*(1/F + 1 + 3*F)) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, from 1st formula *)
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PROG
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(PARI) q='q+O('q^50); F =q*eta(q^3)*eta(q^33)/(eta(q)*eta(q^11)); Vec(-11 + (1 + 3*F)^2*(3*F + 1 + 1/F)) \\ G. C. Greubel, May 10 2018
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CROSSREFS
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KEYWORD
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sign,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 05 2000
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STATUS
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approved
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